The transfer characteristics modelisation of the Mosfet's structure allows us to simulate the doping effect, the grains size, the layer thickness as well as others parameters of the transistor. The purpose of this work is to study the effect of the layer thickness on the carrier's mobility in the channel. For that, a two-dimensional modelling of the electrical conduction in amorphous silicon Mosfet's is used. It is based on the solving of Poisson's equation and the two continuity current equations of electrons and holes, and takes into account of the properties of polysilicon material, such as a density of trapped states formed by two exponential band tails, and gaussian state distribution for the charge carriers. The numerical model assumes a drift- diffusion mechanism in the crystalline regions in series with a thermionic emission mechanism for carriers overcoming the grain boundary potential barrier. In order to validate the conduction model, we also incorporate the effect of the electrical field on the generation carriers at grain boundary traps. The transfer characteristics are studied in function of film thickness, then the carrier's mobility. The results show that, the surface field affects only the low thicknesses, the variation of this field as a fucntion of film thickness is sufficient to expalin the behaviour of channel mobility. For high thicknesses, the field effect mobility is controlled by intergranular barriers of potential.